Question

me ajudaaa de a soma dos 100 primeiros termos pares de uma pá em que a 1=2

Answer 1

$> resolucao \\ \\ \geqslant progressao \: aritmetica \\ \\ an = a1 + (n - 1)r \\ an = 2 + (100 - 1)2 \\ an = 2 + 99 \times 2 \\ an = 2 + 198 \\ an = 200 \\ \\ \\ \geqslant soma \: dos \: termos \: da \: pa \\ \\ sn = \frac{(a1 + an)n}{2} \\ \\ sn = \frac{(2 + 200)100}{2} \\ \\ sn = \frac{202 \times 100}{2} \\ \\ sn = 202 \times 50 \\ \\ sn = 10100 \\ \\ > < > < > < > < > < > < > < >$

Answer 2

$\Large\boxed{\begin{array}{l}\underline{\rm C\acute alculo\,do\,cent\acute esimo\,termo\,par:}\\\sf (0,2,4,6\dotsc)\\\sf r=2-0=2\\\sf a_{100}=a_1+99r\\\sf a_{100}=0+99\cdot2\\\sf a_{100}=198\\\underline{\rm Soma\,dos\,termos\,de\,uma\,PA}\\\sf S_n=\dfrac{n\cdot(a_1+a_n)}{2}\\\\\sf S_{100}=\dfrac{100\cdot(0+a_{100})}{2}\\\\\sf S_{100}=\dfrac{\diagdown\!\!\!\!\!\!10\backslash\!\!\!0\cdot198}{\backslash\!\!\!2}\\\\\sf S_{100}=50\cdot198\\\\\sf S_{100}=9900\end{array}}$